The blazar 3C 345 is similar to the gamma-ray blazar 3C 279 in many aspects, but EGRET did not detect any gamma-rays from 3C 345. We investigate this issue by comparing 3C 345 with 3C 279 and 3C 273, another strong gamma-ray blazar, in the following aspects: the optical (4400 Å) and radio (8 GHz, 22 GHz, and 37 GHz) variability amplitude, the optical shortest variability timescale, and the time lags among variations in the four bands. However, we do not find any significant differences between 3C 345 and the other two sources. This suggests that the differences in the gamma-ray properties may result from other reasons.